A solution to the pyjama problem
成果类型：
Article
署名作者：
Manners, Freddie
署名单位：
University of Oxford
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-014-0571-7
发表日期：
2015
页码：
239-270
关键词：
摘要：
The pyjama stripe is the subset of consisting of a vertical strip of width around every integer -coordinate. The pyjama problem asks whether finitely many rotations of the pyjama stripe around the origin can cover the plane. The purpose of this paper is to answer this question in the affirmative, for all positive . The problem is reduced to a statement closely related to Furstenberg's Theorem from topological dynamics, and is proved by analogy with that result.